A375632 Expansion of e.g.f. exp(2*x) / (1 - x^3/6 * exp(x)).
1, 2, 4, 9, 28, 122, 624, 3523, 22824, 170948, 1422664, 12856373, 126598036, 1358773886, 15721899652, 194356158823, 2560950546576, 35899907132872, 533099244285136, 8351271711094697, 137675784924101596, 2383758487476054242, 43244905386257120044
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^3/6*exp(x)))) -
PARI
a(n) = n!*sum(k=0, n\3, (k+2)^(n-3*k)/(6^k*(n-3*k)!));
Formula
a(n) = n! * Sum_{k=0..floor(n/3)} (k+2)^(n-3*k)/(6^k*(n-3*k)!).